The effect of time-dependent random mass density field on frequencies of solar sound waves

Nocera

Pelinovsky

2004

Waves in Random Media

We investigate the effect of a space-dependent random mass density field on small amplitude acoustic modes that are settled in a semi-infinite medium of a temperature growing linearly with depth. Using a perturbation method, the dispersion relation is derived in the form of Hill's determinant. Numerical solutions of this equation lead to the following conclusions: (a) a weak random field (with σ eff = 0.05) essentially affects long waves which experience attenuation and a frequency reduction; (b) for a stronger random field (with σ eff = 0.1), high-order sound modes behave as sound waves as they are attenuated and their frequencies are increased; (c) for a sufficiently strong random field (with σ eff = 0.2), mode coupling occurs, as a result of which the dispersive curves cross each other, the sound modes loose their identities, and some modes are amplified. Here σ eff denotes the effective strength of a random field.

Section: Introductionmentioning

confidence: 99%

Frequency and amplitude alterations of sound modes in a space-dependent random mass density field

Nocera

Pelinovsky

2004

Waves in Random Media

“…The power maxima in the frequency spectra are close to the frequencies dictated by the unperturbed dispersion relation ω 0 = c 0 k. Thus, we get only one power maximum for each wavenumber, and most of the energy is concentrated around these frequencies. Previous studies on similar problems show that stochastic perturbations in the medium can lead to shifts in frequency for the power maxima, or for the line profile as a whole (e.g., Murawski et al 2001 (undriven free waves) or Skartlien 2002 (stochastically driven waves, uncorrelated medium and source)). Figure 3 shows (for both cases) the relative frequency shifts (ω − c 0 k)/(c 0 k) of the line profiles for different k. We see that a correlation between the source and the density fluctuations is also manifested in the frequency shifts.…”

Section: Numerical Resultsmentioning

confidence: 99%

Numerical simulations of stochastically excited sound waves in a random medium

Selwa

Skartlien

2004

A&A

Self Cite

Abstract. In turbulent acoustic media such as the solar envelope, both wave sources and the propagation characteristics (background density, refractive index, dissipation, etc.) are stochastic quantities. By means of numerical simulation of the Euler equations, we study two cases in a homogeneous stochastic medium in which the background density fluctuations and wave sources are 1) correlated and 2) uncorrelated. We find that in the uncorrelated case, the coherent (or mean) acoustic field is zero, leaving only an incoherent field. In the correlated case, the coherent field is nonzero, yielding both coherent and incoherent fields. We question the use of mean-field dispersion relations to determine frequency shifts in p-mode and f-mode spectra, since the coherent field can be non-existent or weak relative to the incoherent field. We demonstrate the importance of accounting for a stochastic wave source by showing that the two cases give very different frequency shifts.

“…[2,11]) at equilibrium which consists of the non-random uniform quantities 0 = constant, p 0 = constant, and random mass density r (x, t) and velocity V r (t) fields:…”

Section: Numerical Model For Sound Waves In Random Fieldsmentioning

confidence: 99%

“…As the shortest waves are affected most by a random field [2] we expect that pulses will be altered by the presence of a random field. For instance, in a random medium a pulse will generally be shifted to a different spatial position and its amplitude will be altered.…”

Section: Numerical Model For Sound Waves In Random Fieldsmentioning

confidence: 99%

See 1 more Smart Citation

One-dimensional numerical simulations of random sound impulses

Mędrek²

2003

Waves in Random Media

We perform one-dimensional numerical simulations of small-amplitude acoustic pulses in space-and time-dependent random mass density and timedependent velocity fields. Numerical results reveal that: (a) random fields affect the speeds, amplitudes and, consequently, shapes of sound pulses; (b) for weak random fields and short propagation times the numerical data converge with the analytical results of the mean field theory which says that a space-dependent (time-dependent) random field leads to wave attenuation (amplification) and all random fields speed up sound pulses; (c) for sufficiently strong random fields and long propagation times numerical simulations reveal pulse splitting into smaller components, parts of which propagate much slower than a wave pulse in a non-random medium. These slow waves build an initial stage of a wave localization phenomenon. However, this effect can be very weak in a real three-dimensional medium.